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Note therefore that this function should only be applied to unit\n // vectors so z > 1 should not exist\n const zClamp = Math.min(Math.max(z, -1), 1);\n const lat = radiansToDegrees(Math.asin(zClamp));\n const lng = radiansToDegrees(Math.atan2(y, x));\n\n return [lng, lat];\n}\n\nfunction nearestPointOnSegment(\n posA: Position, // start point of segment to measure to\n posB: Position, // end point of segment to measure to\n posC: Position // point to measure from\n): [Position, boolean] {\n // Based heavily on this article on finding cross track distance to an arc:\n // https://gis.stackexchange.com/questions/209540/projecting-cross-track-distance-on-great-circle\n\n // Convert spherical (lng, lat) to cartesian vector coords (x, y, z)\n // In the below https://tikz.net/spherical_1/ we convert lng (𝜙) and lat (𝜃)\n // into vectors with x, y, and z components with a length (r) of 1.\n const A = lngLatToVector(posA); // the vector from 0,0,0 to posA\n const B = lngLatToVector(posB); // ... to posB\n const C = lngLatToVector(posC); // ... to posC\n\n // The axis (normal vector) of the great circle plane containing the line segment\n const segmentAxis = cross(A, B);\n\n // Two degenerate cases exist for the segment axis cross product. The first is\n // when vectors are aligned (within the bounds of floating point tolerance).\n // The second is where vectors are antipodal (again within the bounds of\n // tolerance. Both cases produce a [0, 0, 0] cross product which invalidates\n // the rest of the algorithm, but each case must be handled separately:\n // - The aligned case indicates coincidence of A and B. therefore this can be\n // an early return assuming the closest point is the end (for consistency).\n // - The antipodal case is truly degenerate - an infinte number of great\n // circles are possible and one will always pass through C. However, given\n // that this case is both highly unlikely to occur in practice and that is\n // will usually be logically sound to return that the point is on the\n // segment, we choose to return the provided point.\n if (segmentAxis[0] === 0 && segmentAxis[1] === 0 && segmentAxis[2] === 0) {\n if (dot(A, B) > 0) {\n return [[...posB], true];\n } else {\n return [[...posC], false];\n }\n }\n\n // The axis of the great circle passing through the segment's axis and the\n // target point\n const targetAxis = cross(segmentAxis, C);\n\n // This cross product also has a degenerate case where the segment axis is\n // coincident with or antipodal to the target point. In this case the point\n // is equidistant to the entire segment. For consistency, we early return the\n // endpoint as the matching point.\n if (targetAxis[0] === 0 && targetAxis[1] === 0 && targetAxis[2] === 0) {\n return [[...posB], true];\n }\n\n // The line of intersection between the two great circle planes\n const intersectionAxis = cross(targetAxis, segmentAxis);\n\n // Vectors to the two points these great circles intersect are the normalized\n // intersection and its antipodes\n const I1 = normalize(intersectionAxis);\n const I2: Vector = [-I1[0], -I1[1], -I1[2]];\n\n // Figure out which is the closest intersection to this segment of the great circle\n // Note that for points on a unit sphere, the dot product represents the\n // cosine of the angle between the two vectors which monotonically increases\n // the closer the two points are together and therefore determines proximity\n const I = dot(C, I1) > dot(C, I2) ? I1 : I2;\n\n // I is the closest intersection to the segment, though might not actually be\n // ON the segment. To test whether the closest intersection lies on the arc or\n // not, we do a cross product comparison to check rotation around the unit\n // circle defined by the great circle plane.\n const segmentAxisNorm = normalize(segmentAxis);\n const cmpAI = dot(cross(A, I), segmentAxisNorm);\n const cmpIB = dot(cross(I, B), segmentAxisNorm);\n\n // When both comparisons are positive, the rotation from A to I to B is in the\n // same direction, implying that I lies between A and B\n if (cmpAI >= 0 && cmpIB >= 0) {\n return [vectorToLngLat(I), false];\n }\n\n // Finally process the case where the intersection is not on the segment,\n // using the dot product with the original point to find the closest endpoint\n if (dot(A, C) > dot(B, C)) {\n // Clone position when returning as it is reasonable to not expect structural\n // sharing on the returned Position in all return cases\n return [[...posA], false];\n } else {\n return [[...posB], true];\n }\n}\n\nexport { nearestPointOnLine };\nexport default nearestPointOnLine;\n"]}